sid_m40

“To minimize B''s time, we must maximize A''s time.
Since each machine can work for at most 8 hours, let A''s time = 8 hours.
Since A''s rate = 9000 pencils per hour, the number of pencils produced by A in 8 hours = rt = 9000*8 = 72,000.
Remaining pencils = 100,000 - 72,000, = 28,000.
Since ...”

“Test the THRESHOLD.
In the question stem, the threshold is 40 CHAIRS.
The total cost of 40 chairs = 40*50 = 2000.
Statement 1: The total price of the desks and chairs is 5,000.
It is possible that 40 chairs are purchased (at a total cost of $2000) or that MORE CHAIRS are purchased.
...”

“Monthly food expense except in January:
Let y=$2.
Discount in January:
Let x=100%.
Since $2 is spent each month for 8 of the first 9 months, the total spent during these 8 months = 8*2 = 16.
Since food purchases are 100% lower in January -- implying that they are FREE in January -- the amount ...”

“Alternate approach:
To determine the ratio of birds to dogs, plug in a TEST VALUE for the total number of pets.
Let b = the number of birds and d = the number of dogs.
Let the test value for the total number of pets = the LCM of 3 and 5 = 15.
Since 1/5 are birds, b = 1/5 * 15 = 3.
Since 1/3 ...”

“Statement 1:
If d=72, then t = d/r = 72/72 = 1 hour.
If d=144, then t = 144/72 = 2 hours.
Since the time can be different values, INSUFFICIENT.
Statement 2:
Time and rate have a RECIPROCAL RELATIONSHIP:
If the time is cut in HALF, then the rate DOUBLES.
If the time DOUBLES, then the ...”

“Let G = the gas in the tank and C = the capacity of the tank.
Statement 1:
G - (1/2)G = (1/3)C
No way to solve for G.
INSUFFICENT.
Statement 2:
G + 0.75 = C
No way to solve for G.
INSUFFICIENT.
Statements combined:
Since we have two variables (G and C) and two distinct linear ...”

“Here, the value in red is the sum of Jake''s weight and TWICE the sister''s weight:
187 + 2(89.5) = 366.
But the prompt gives an integer value for the sum of Jake''s weight and the sister''s ACTUAL weight -- a constraint that forces Jake''s weight to be an even integer.”

“The sum of Jake''s weight and his sister''s weight is an INTEGER VALUE.
The answer choices indicate that Jake''s weight is an INTEGER VALUE.
Implication:
The sister''s weight must also be an integer value.
Thus, the value in red -- 89.5 -- is not a valid option for the sister''s weight.
Given ...”

“Let the river''s rate = 1 mph and the boat''s rate = 5 mph.
When the boat travels DOWNRIVER, the boat and the river WORK TOGETHER, so we ADD their rates:
5+1 = 6 mph.
When the boat travels UPRIVER, the boat and the river COMPETE, so we SUBTRACT their rates:
5-1 = 4 mph.
Rate and time have ...”

“ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.
If Jake loses 8 pounds, he will weigh twice as much as his sister.
j-8 = 2s
j = 2s + 8 = even + even = even.
Since Jake''s weight must be an EVEN VALUE, the correct answer is E.”

“Let S = Sara''s age.
Sum of the ages = 2+4+5+8+10+13+S = 42+S.
Statement 1:
Since the average age is equal to an INTEGER -- the fourth largest age -- we get:
Sum of the ages = (number of ages)(average age) = (7)(INTEGER) = multiple of 7.
The blue expression and the red expression each ...”

“We can PLUG IN THE ANSWERS, which represent the value of m.
When the correct answer is plugged in, the median will be equal to the range.
Note:
When the prompt includes the phrase which of the following, the correct answer is likely to be D or E.
E: m=3
Resulting set: 1, 1, 2, 2, m=3, 3, 3, ...”

“Let X=8 and Y=4.
Henry eats X scones in X percent of the time it takes Rachel to eat Y scones.
Since Henry eats X=8 scones in 8% of the time it takes Rachel to eat Y=4 scones -- 10 minutes, according to the prompt -- the time for Henry to eat 8 scones = 8% of 10 minutes = (8/100)(10) = 4/5 ...”

“Consider the following equation:
7x + 5y = 70.
If x and y are nonnegative integers, the following solutions are possible:
x=10, y=0
x=5, y=7
x=0, y=14.
Notice the following:
The value of x changes in increments of 5 (the coefficient for y).
The value of y changes in increments of ...”

“x is directly proportional to y implies the following:
x/y = k.
x = ky.
In each case, k is a CONSTANT.
The cost of a square slab is proportional to its thickness and also proportional to the square of its length.
Thus:
c = k * T * L².
What is the cost of a square slab that is 3 meters ...”

“species may be singular or plural.
Passage:
Planting trees primarily from the species that turns out to have the best record of survival will assure downtown Thomasville of an abundant tree population 20 years from now.
Here, the verb attributed to species is turns.
Since turns is singular, ...”

“(number of machines)(number of hours) = number of toys that are produced.
In the prompt above, the blue values are THE SAME.
Implication:
2 machines take h+3 hours to produce the same number of toys as 3 machines in 2 hours:
2(h+3) = 3h
2h + 6 = 3h
6 = h.
Since 3 machines produce 360 toys ...”

“Let x = 5 seconds for the first lap, implying 10 seconds for the second lap, 3 seconds for the third lap, and a total of 18 seconds for all 3 laps.
(18 seconds)/(3 laps) = (6 seconds)/(1 lap) = 1/10 minute per lap.
The correct answer must yield a value of 1/10 when x=5.
Only D works:
(x+1)/60 ...”

“The information in red is irrelevant.
Only the following facts matter:
Ross travels onward at a rate of 1 mile every 12 minutes.
He travels home for twice the onward distance at half the onward speed.
Onward speed = 1 mile per 12 minutes = 5 miles per 60 minutes = 5 mph.
Let the onward ...”

“The original total cost of the 10 pieces of fruit = 10*56 = 560.
According to the answers, after 1, 2, 3, 4, or 5 oranges are removed -- so that 9, 8, 7, 6, or 5 pieces of fruit remain -- the average cost per piece decreases to 52.
Since the original total cost is a multiple of 10, and the price ...”

“Let x = the product of the two denominators in the prompt = 3*4 = 12.
Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4.
Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for ...”

“Given two sides of a triangle, the greatest possible area will be achieved if the two sides form a RIGHT ANGLE and serve as the triangle''s base and height.
For the problem above, I posted an illustrated solution here:
...”

“When the SAME DISTANCE is traveled at two different speeds, the average speed for the entire trip will be CLOSER TO THE LOWER SPEED than to the higher speed.
The reason:
The portion traveled at the lower speed takes LONGER.
Since more time is spent at the lower speed than at the higher speed, the ...”

“Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9.
No way to determine the exact number of staff members.
INSUFFICIENT.
Statement 2: ...”

“Both of the following are viable:
Vehicles powered by natural gas emit less of certain pollutants than those burning gasoline or diesel fuel.
Vehicles powered by ndatural gas emit less of certain pollutants than do those burning gasoline or diesel fuel.
The inclusion of do is optional.
With or ...”

“What is the value of n-m?
(m,0) and (n,0) are the two points where y=0 and the graph intersects the x-axis.
Thus, m and n are the x-intercepts of the graph.
Since m < n, n-m > 0.
Question rephrased: What is the positive difference between the x-intercepts?
Statement 1: 4b = a²-4
Test ...”

“percent may serve as a NOUN.
Of the students in the class, eighty percent passed the test.
Here, eighty percent is a NOUN serving as the subject of passed.
twice is a MODIFIER.
It cannot serve as the subject of a sentence.
Of the students in the class, twice passed the test.
The sentence ...”

“Consider the following equation:
5x + 7y = 70.
If x and y are nonnegative integers, the following solutions are possible:
x=0, y=10
x=7, y=5
x=14, y=0.
Notice the following:
The value of x changes in increments of 7 (the coefficient for y).
The value of y changes in increments of 5 (the ...”

“The ratio of milk and water in a mixture is 2:1,
Let milk = 2 liters and water = 1 liter.
Some quantity of water is added to the mixture to make the ratio of milk and water in the new mixture 1:2.
Since the resulting amount of water must be double the original 2 liters of milk, the resulting ...”

“Let the 7 cars be A, B, C, D, P, Q and S.
Since P and Q must occupy adjacent positions, consider PQ a single element in the arrangement.
The number of ways to arrange the 6 elements A, B, C, D, PQ and S = 6! = 720.
In 1/2 of these arrangements, S will be to the LEFT of PQ.
In the ...”

“Let:
W = the total number of white marbles.
E = the total number of even marbles.
WE = the total number of white even marbles.
Statement 1:
Thus, WE = 0.
No way to determine the value of W or E.
INSUFFICIENT.
Statement 2:
Implication:
W-E = (0.2)(25) = 5.
Case 1: W=10, E=5, WE=0
...”

“Statement 2: Brittany always leaves the hotel at exactly 5.30pm.
To see the situation more clearly, plug in a value for the distance between the hotel and the office.
Let the distance = 6 miles.
Since Allison takes 1 hour -- from 5 to 6pm -- to travel the entire distance, Alison''s rate = d/t = ...”

“It is possible for back-to-back modifiers joined solely by a comma to have the same referent.
Three examples:
http://www.beatthegmat.com/the-hognose-snake-puts-on-an-impressive-bluff-t93558.html
http://www.beatthegmat.com/parallelism-issue-t96011.html
...”

“The usage of the term arrangements is misleading. The prompt seems intended to ask the following:
The first player selected can be paired with any of the 5 other players.
Thus, the number of options for the first player selected = 5.
At this point, 4 players remain.
The next player ...”

“The determine the percent decrease, we need to know the RATIO between the remaining amount of sugar after cookie-making and the original amount of sugar.
Statement 1:
Case 1: Remaining sugar after cookie-making = 10 pounds
Since the remaimning amount of sugar would need to increase by 30% to ...”

“Statement 1: The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
Case 1: Distance between Townsend and Smallville = 80 miles
Time to travel from Townsend to Smallville at a speed of 40 mph = 80/40 = 2 hours.
Time to travel from Smallville to Townsend = ...”

“Let x = the number of 100-point labs and y = the number of 85-point labs.
Question stem, rephrased:
What is the value of x?
Statement 1:
100x + 85y = 1140
20x + 17y = 228
The value in blue implies the following:
Since 20x will have a units digit of 0, 17y must have a UNITS DIGIT OF 8.
...”

“Alternate approach:
Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0.
If x²-6=x, we get:
x²-x-6=0
(x-3)(x+2) = 0
Only the factor in green implies a nonnegative option for x:
x-3=0
x=3.
The correct ...”

“The usage of number implies that we should consider NON-INTEGER values.
Both statements are satisfied by z=18.1 and z=19.1
Since the units digit of z can be different values, the two statements combinecd are INSUFFICIENT.
The correct answer is E.”

“Any BAG taken on the subway IS subject to search by the police.
Any BAGS taken on the subway ARE subject to search by the police.
In each of these sentences, any is a MODIFIER describing the subject in blue.
In the first sentence, the verb (is) is SINGULAR to match the singular subject in blue.
...”

“Statement 1:
No information about Charlie or Daryl.
INSUFFICIENT.
Statement 2:
For every 2 home run hits made by Charlie and Daryl combined, Brady made 4 home run hits, implying that Brady made 4 of every 6 home run hits:
4/6 = 2/3.
SUFFICIENT.
The correct answer is B.”

“Downhill speed - uphill speed = (x+10) - (x-8) = 18.
Implication:
The downhill speed is 18 mps greater than the uphill speed.
We can PLUG IN THE ANSWERS, which represent the downhill speed.
Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...”

“Statement 1:
To MINIMIZE the number of coins so that a sum of 170 cents is yielded by at most 8 coins, we must MAXIMIZE the number of quarters.
Since 7*25 = 175 cents, the number of quarters must be less than 7.
170 cents will be yielded by 6 quarters (totaling 150 cents) and 2 dimes (totaling 20 ...”

“Let the tank = 36 gallons.
Since the first pipe takes 3 hours to fill 1/2 the tank -- and (1/2)(36) = 18 gallons -- the rate for the first pipe = w/t =18/3 = 6 gallons per hour.
Since the second pipe takes 6 hours to fill 2/3 of the tank -- and (2/3)(36) = 24 gallons -- the rate for the second ...”

“Strategy:
Try to show that four of the answer choices do NOT have to be positive.
Case 1: x=1 and y=1
In this case, A, B and D are not positive.
Eliminate A, B and D.
Case 2: x=1 and y=2
In this case, C is not positive.
Eliminate C.
The correct answer is E.”

“Total amount of feed = (number of chickens)(number of days).
The number of chickens is INVERSELY PROPORTIONAL to the number of days.
If the number of chickens DOUBLES, then the feed will last for 1/2 the number of days.
If the number of chickens TRIPLES, then the feed will last for 1/3 the ...”

“Let J = the number of hours that John works.
Since John assembles 3 chairs per hour, the number of chairs assembled by John = 3J.
Let L = the number of hours that Larry works.
Since Larry assembles 4 chairs per hour, the number of chairs assembled by Larry = 4L.
Since John and Larry work a total ...”

“Number of options for Phoebe = 1. (Must be Margherita.)
Number of options for Ross = 3. (Of the 4 remaining pizzas, any but Hawaiian.)
Number of options for Chandler = 3. (Any of the 3 remaining pizzas.)
Number of options for Joey = 2. (Either of the 2 remaining pizzas.)
Number of options for ...”

“One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time.
Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 ...”

“This is a MIXTURE problem.
Two speeds (3 mph and 8 mph) are combined to form a mixture with an average speed of 4 mph.
To determine how much time must be spent at each speed, we can use ALLIGATION.
Let U = the uphill speed and D = the downhill speed.
Step 1: Plot the 3 speeds on a number ...”

“2 and 17 have no factors in common.
Since n must be divisible by both 2 and 17 -- and 2*17 = 34 -- n must be a MULTIPLE OF 34.
Thus, n must be divisible by I.
Eliminate any answer choice that does not include I.
Eliminate B and E.
If n=34, then n is not divisible by II or III.
Eliminate any ...”

“To keep track of the number of options for each position, draw a TREE.
Start with the MOST RESTRICTED position, which is SWEEPER.
If Sweeper = 3, then Goalie = 5.
If Sweeper = 4, then Fullback = 2.
Here''s the tree so far:
http://s11.postimage.org/laxnlsbof/soccer_half_tree.jpg
Now complete ...”

“A group...EACH has a team.
The wording above does not convey a logical meaning.
When each serves as an adverb, it cannot refer to a singular noun such as a group.
When each serves as an adverb, it may refer only to a PLURAL noun.
The prompt seems intended to convey the following:
Since ...”

“Statement 1:
For every $100 commission that Dan earns, Jeff earns $120 in commission.
Since the commission rates for Dan and Jeff are unknown, no way to determine whether Jeff recorded more sales revenue than Dan.
INSUFFICIENT.
Statement 2:
Since Jeff''s sales and Dan''s sales can be any ...”

“Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:
Do the values in set A deviate more from the mean than the do ...”

“x² < y² can be rephrased as follows:
|x| < |y|
Thus, the question stem can be rephrased as follows:
Is |x+10| < |y-10|?
|a-b| = the distance between a and b
|a+b| = |a-(-b)| = the distance between a and -b
Thus, the question stem can be further rephrased as follows:
Is the ...”

“The team has won 58 percent of the games it has played.
58% = 58/100 = 29/50.
The fraction in blue implies that the number of wins must be a MULTIPLE OF 29:
If 50 games are played, the number of wins = (29/50)(50) = 29.
If 100 games are played, the number of wins = (29/50)(100) = 58.
If 150 ...”

“The SC above is modeled -- not altogether successfully -- after SC30 in the OG12:
https://www.beatthegmat.com/not-sure-about-the-answer-of-a-question-from-og12-t265701.html
Rather than study the SC above, stick to the official SC.”

“The values in the chart DOUBLE-COUNT any student who belongs to 2 of the 3 clubs.
The totals for chess and drama -- 40 and 30 -- double-count the 10 students who belong to both chess AND drama.
The totals for chess and math -- 40 and 25 -- double-count the 5 students who belong to both chess AND ...”

“Let r=9, with the result that 1+r = 10.
Her husband can turn each dollar she gives him into 1+r, which will be deposited in a bank account.
Let the wife give the husband $1, implying that the husband turns this $1 into 1+r = $10.
Thus, the amount deposited into the account = $10.
The ...”

“Let the distance between A and B = 120 miles.
Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles.
Since the average speed for the 120-mile leg between A and B = 60 ...”

“The sum for Lisa and Mike is 50 less than the sum for Norm and Mike.
Since Mike is common to both sums, the 50-photo difference must be yielded solely by Lisa and Norm.
Implication:
Lisa took 50 fewer photos than Norm.
We can PLUG IN THE ANSWERS, which represent the number of photos taken ...”

“Let h=3.
Since an average of $78 is sold per hour, the total revenue for 3 hours = 3*78 = 234.
Since the cost for the day is composed of $150 for the table rental and $10 per hour for the assistant, the cost for the day = 150 + 3*10 = 180.
P = profit = revenue - cost = 234 - 180 = 54.
The ...”

“It takes for granted that X implies that X is an ASSUMPTION: a statement that must be true for the conclusion to hold.
Thus, when X is negated, the conclusion must be invalidated.
B: It takes for granted that the volunteers with the highest levels of self-esteem had better social skills than did ...”

“Premise:
Volunteers with the highest levels of self-esteem consistently rated themselves as having much better social skills than did the volunteers with moderate levels.
Conclusion:
Attaining an exceptionally high level of self-esteem greatly improves one’s social skills.
The correct answer ...”

“Let k=10.
2k years ago Frank was 3k years old.
Since k=10, 20 years ago Frank was 30 years old, implying that his age now = 30+20 = 50.
In k years Frank''s age, in years, will be:
Since Frank is now 50 years old, Frank''s age in 10 years = 50+10 = 60.
The correct answer must yield a value ...”

“Alternate approach:
For any quadratic in the form x² + bx + c = 0, where b and c are rational numbers:
If one of the roots is m+√n, then the other root is m-√n.
Sum of the roots = -b
Product of the roots = c
Here, since one of the roots is 1+√2, the other root is 1-√2.
Thus:
-b ...”

“Since each payday is $10 more than the preceding payday, the list of 15 paydays constitutes an EVENLY SPACED SET.
Statement 1:
For any evenly spaced set:
Median = Sum/Quantity.
Thus:
Pay on the 14th day = median of the 3 most recent days = sum/quantity = 690/3 = 330.
Since the pay on the ...”

“Original deposit: 10,000.
The balance doubles every 10 years.
After 10 years, we get:
2*10,000 = 20,000.
After 20 years, we get:
2*20,000 = 40,000.
After 30 years, we get:
2*40,000 = 80,000.
The correct answer is E.”

“Let the 6 vertices = A, B, C, D, E and F.
P(the triangle includes AT LEAST 1 side of the hexagon) = 1 - P(the triangle includes NO sides of the hexagon).
From the 6 vertices, the number of ways to choose 3 to form a triangle = 6C3 = (6*5*4)/(3*2*1) = 20.
Of these 20 triangles, only 2 include ...”

“Number of options for the 1st person = 8.
Number of options for the 2nd person = 6. (Of the 7 people left, we can''t use the twin of the 1st person chosen, leaving 7-1= 6 choices.)
Number of options for the 3rd person = 4. (Of the 6 people left, we can''t use the twins of the 2 people already ...”

“Let x = the yearly increase.
Height after 4 years = 4 + 4x.
Height after 6 years = 4 + 6x.
At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year.
The phrase in red implies the following:
The height in the 6th year was 6/5 of the height in the 4th ...”

“Any integer that is a multiple 10 is also a multiple of 5.
Implication:
Any integer that satisfies Statement 1 will also satisfy Statement 2.
Both statements are satisfied by the following cases:
Case 1: p=10, which is a multiple of 10 (and thus is also a multiple of 5)
In this case, p is NOT a ...”

“The drawings below satisfy both statements:
http://s4.postimage.org/1yjxdhskk/ABCD_number_line.jpg
Since in the first case BD=1 and in the second case BD=17, the two statements combined are insufficient.
The correct answer is E.”

“Case 1: Team A wins a prize, with the result that Team B must win a prize
Number of prizes that could be won by A = 3.
Number of remaining prizes that could be won by B = 2.
Number of teams that could win the third prize = 4. (Any of the 4 remaining teams.)
To combine these options, we ...”

“Let n=50, implying that 50% of the sold juice packs are A, while the other half are B.
In other words, the store sells an EQUAL NUMBER of each type of juice pack.
Let the store sell 2 OF EACH TYPE of juice pack.
Revenue from two $1 packs of A = 2*1 = 2.
Revenue from two $1.5 packs of B = ...”

“Let James'' rate = 3 mph.
James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James ...”

“The equation for a circle with its center at the origin and a radius of r is as follows:
x² + y² = r².
Thus, x² + y² = 25 is a circle with its center at the origin and a radius of 5.
A point on this circle will have integer coordinates in three cases:
Case 1: The radius is horizontal
...”

“The average speed -- 2.8 miles per hour -- must be BETWEEN the two individual rates (s and s+1).
Thus, s = 2 miles per hour and s+1 = 3 miles per hour.
We can PLUG IN THE ANSWERS, which represent the fraction traveled at 2 miles per hour.
When the correct fraction is plugged in, the average ...”

“Number of options for president = 10. (Any of the 10 members.)
From the remaining 9 members, the number of ways to choose 2 to serve as vice-president = 9C2 = (9*8)/(2*1) = 36.
To combine these options, we multiply:
10*36 = 360.
The correct answer is E.”

“One approach is to use the following equation:
(machines)(time) / output = (machines)(time) / output
In the equation above:
Machines and time are INVERSELY PROPORTIONAL.
As the number of machines increases, the amount of time required to produce the same output decreases.
Machines and ...”

“One approach:
Good Cases = Total Cases - Bad Cases.
Total Cases:
From 9 points, the number of ways to choose 3 = 9C3 = (9*8*7)/(3*2*1) = 84.
Bad Case 1: Choosing 3 collinear points from the 5-point line, with the result that a triangle cannot be formed
From the 5 points on this line, the ...”

“Since the prompt indicates that n is an integer greater than 1, the case in red is not possible.
The only value that satisfies Statement 2 is n=2, making Statement 2 SUFFICIENT.
The correct answer thus is not C but B.”

“Between 1982 and 1987 are 4 non-leap years and 1 leap year.
Each non-leap year is composed of 365 days; a leap year is composed of 366 days.
Thus, from June 25, 1982 to June 25, 1987, the total number of days = 4(365) + 366.
Since June 25, 1982 is a Friday, every passing of 7 days will yield ...”

“(man''s rate)/(woman''s rate) = (4 mph)/(20 mph) = 1/5.
Between the moment when the woman passes the man and the moment when she stops to wait, the woman and the man each travel for 5 minutes.
During these 5 minutes, the woman travels x miles.
Since the man''s rate is 1/5 the woman''s rate, the ...”

“Statement 1:
Here, n can be any prime number.
INSUFFICIENT.
Statement 2:
(n+2)/n = n/n + 2/n = 1 + 2/n.
Given that n must be an integer, 1 + 2/n will yield an integer value only if n is a FACTOR OF 2.
Factors of 2: 1 and 2.
Since n must be greater than 1, n=2.
SUFFICIENT.
The correct ...”

“Statement 1:
Rate and time have a RECIPROCAL relationship.
A rate ratio of (40kph) : (50kph) = 4:5 implies a time ratio of 5:4 = 10:8.
The time ratio in blue implies that -- for the time at 40kph to be 2 hours more than the time at 50kph -- the time at 40kph must be 10 hours, while the time at ...”

“Statement 1:
The TIME RATIO for Tim and Glenn = 48:60 = 4:5.
Since time and rate have a RECIPROCAL relationship, the RATE RATIO for Tim and Glenn = 5:4.
Implication:
For every 5 laps that Tim runs, Glenn runs only 4 laps.
Thus, after running 5 laps, Tim will have run 1 more lap than Glenn. ...”

“Let the one-bedroom rent = $2 per month, implying that the two-bedroom rent = 2 + (50% of 2) = 2 + 1 = $3 per month.
Since the rent for a one-bedroom apartment = $2 per month, the total amount to rent a one-bedroom apartment for 12 months = 2*12 = $24.
For $24, the number of months yielded for a ...”

“Let W = Winesap crates, M = McIntosh crates, and R = Roma crates.
Since a total of 25 crates are ordered, we get:
W + M + R = 25.
To MINIMIZE the value of W, we must MAXIMIZE the values of M and R.
Since the store is to order more crates of Winesap than crates of McIntosh and more crates of ...”

“The prompt states:
Every day, the two machines operate constantly from 08:00 to 18:00.
As shown in my post above, Statement 2 yields the following rate ratio:
(W alone) : (W and D together) = 1:5.
The rate ratio indicates that -- of every 5 kg produced when W and D work together from 8:00 to ...”

“Generally, for + VERBing is an ADJECTIVE serving to modify a NOUN.
A: The Breeding Bird Survey uses annual roadside counts along established routes for monitoring.
Here, for monitoring seems to be an ADJECTIVE modifying routes, implying that the ROUTES were designed FOR MONITORING.
Not the ...”

“Let x = the two-digit number.
Since dividing by 4 leaves a remainder of 1, x is equal to one more than a multiple of 4:
x = 4k + 1
Since dividing by 14 leaves a remainder of 1, x is equal to one more than a multiple of 14:
x = 14m + 1
Since the two expressions in blue must be equal, we ...”

“Statement 1: If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400
When the selling price per coat is doubled, the resulting profit per coat = (total profit)/(number of coats) = 2400/20 = 120.
Case 1: Double the selling price = ...”

“60! = 60*59*58*....*3*2*1.
Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 60! will yield a 0 at the end of the integer representation of 60!.
The prime-factorization of 60! is composed of FAR MORE 2''S than 5''s.
Thus, the number of 0''s depends on the ...”

“An INSCRIBED ANGLE is formed by two chords.
A CENTRAL ANGLE is formed by two radii.
When an inscribed angle and a central angle intercept the same two points on a circle, the inscribed angle is 1/2 the central angle.
https://i.postimg.cc/qgbxWKdW/Angle-CEB-1.png
Here, inscribed angle CFB and ...”

“Statement 1: x=12u, where u is an integer and x=8y+12.
In other words, x is a multiple of 12.
For x to be a multiple of 12, 8y must be a multiple of 12.
If y=3, then x = 8*3 + 12 = 36.
The GCD of 3 and 36 is 3.
If y=6, then x = 8*6 + 12 = 60.
The GCD of 6 and 60 is 6.
Since the ...”

“Time and rate have a RECIPROCAL RELATIONSHIP:
2 times as fast implies 1/2 the time.
3 times as fast implies 1/3 the time.
Let t = the normal time.
Since the bus travels today at 7/6 its normal rate, the time today is equal to 6/7 of the normal time:
(6/7)t.
Since the bus leaves 1/2 hour late ...”

“Given any set that is symmetrical about the median:
Sum = (quantity)(median)
The set of 3-digit integers that can be formed from the digits 1,2 and 3 is symmetrical about the median (222):
...212, 213, 221, 222, 223, 231, 232...
Thus:
Sum of the 27 integers = (quantity)(median) = 27*222 = ...”

“For the purposes of a Y/N DS problem, the rephrase is the equivalent of the original question stem.
Original question stem: Is x² > xy?
The answer will be YES if y/x is less than 1..
The answer will be NO if y/x is NOT less than 1.
Thus, the original question stem can be rephrased as ...”

“x² > xy is true only if x is NONZERO, in which case we can safely divide by x², since the square of a nonzero value must be positive:
x²/x² > (xy)/x²
1 > y/x
Question stem, rephrased:
Is y/x < 1?
Statement 1: x > y
If x=2 and y=1, then y/x =1/2. so the answer to the ...”

“Let the job = the LCM of the 3 times = 60 widgets.
Maximum time:
The maximum time is yielded when the slowest person -- R -- works alone.
Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours.
Minimum time:
The minimum time is yielded when all 3 people work ...”

“X led to Y implies that X did not directly cause Y but that X was a factor that helped to yield Y.
SC755 in the OG17:
An inability to adapt led to their extinction.
Here, an inability to adapt did not directly cause the extinction but was a factor that helped to yield the extinction.
A cause ...”

“Generally, COMMA + as-clause implies that the clause after as LEADS to the preceding clause, with the result that the two clauses happen concurrently.
An OA in GMATPrep:
The steel industry has changed radically over the last two decades, as large, integrated companies such as Bethlehem Steel have ...”

“Let B = Barry''s rate and W = the walkway''s rate.
The distance can be ANY VALUE.
Let the distance = 240 meters.
WITH the walkway, the time = 30 seconds:
Here, Barry and the walkway WORK TOGETHER, so we ADD their rates:
B+W = d/t = 240/30 = 8 meters per second.
AGAINST the walkway, the ...”

“Let the x family members = the product of the two denominators = 3*7 = 21.
Number who chose to have a hamburger = (1/3)(21) = 7.
Since 1/7 of the hamburger-eaters also had a hot dog, the number who had both = (1/7)(7) = 1.
Thus, the number who did NOT have both = (total members) - (number who had ...”

“I believe that the prompt above is outdated; regardless, it does not list a correct answer. The prompt below appears in Manhattan''s 5 lb. Book of GRE Practice Problems:
Case 1: 57XXX
Number of options for the hundreds digit = 10. (Any digit 0-9.)
Number of options for the tens digit = 10. ...”

“Since the N cookies can be divided evenly among 24 or 18 students, N must be divisible by both 24 and 18.
One way to determine the LCM of two integers is to take multiples of the LARGER integer until we get a multiple of the SMALLER integer.
Multiples of 24:
24, 48, 72...
We can stop here: the ...”

“Statement 1:
If NONE of the members sells at least 2 tickets, then the 3 members sell a maximum of 1 ticket each, yielding the following total:
1+1+1 = 3.
Too small, since the total number of tickets sold = 6.
Implication:
For a total of 6 tickets to be sold, one of the 3 members must sell at ...”

“This is a weighted average/mixture problem.
Average score for the first N games = 35.
Score for the final game = 28.
Average score for the MIXTURE of all the games = 34.
Step-by-step instruction for the alligation approach:
Step 1: Plot the 3 averages on a number line, with the average ...”

“The difference between the endpoints of the range = 200-10 = 190.
Since neither endpoint is a multiple of 3, we can count the multiples of 3 simply by dividing 3 into 190:
190/3 ≈ 63.
The correct answer is D.”

“Let d=100.
After the value of the stock increases by 40% to $140, the share received by each of the 20 friends = 140/20 = 7.
The correct answer must yield a value of 7 when d=100.
Only E works:
(7d)/100 = (7*100)/100 = 7.
The correct answer is E.”

“We can PLUG IN THE ANSWERS and use alligation.
To learn about alligation, check my posts here:
https://www.beatthegmat.com/statistics-average-question-t288903.html
https://www.beatthegmat.com/alligation-method-t293459.html
https://www.beatthegmat.com/mean-t266852.html
Let O = the original ...”

“Statement 1:
Time and rate have a RECIPROCAL relationship.
Since X and Y together take 2/3 as long as Y alone, X and Y together work 3/2 as fast as Y alone.
Thus, if Y''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that X''s rate alone = ...”

“To form a triangle, we must select 3 points such that at most 2 are collinear.
Case 1: Select 3 points not on the x-axis
From the 4 points not on the x-axis, the number of ways to choose 3 = 4C3 = (4*3*2)/(3*2*1) = 4.
Case 2: Select 1 point on the x-axis and two points not on the x-axis
From ...”

“Number of options for president = 8. (Any of the 8 candidates.)
Number of options for treasurer = 7. (Any of the 7 remaining candidates.)
From the 6 remaining people, the number of ways to choose 3 to serve as warrant officers = 6C3 = (6*5*4)/(3*2*1) = 20.
To combine these options, we multiply:
...”

“For the set of pencils to be shared evenly, the total number of pencils must be divisible by the total number of children.
Thus, the correct answer must be divisible by 2, 3, 4, 5 and 6.
Of the five answer choices, only E is divisible by 2, 3, 4, 5 and 6.
The correct answer is E.”

“We can PLUG IN THE ANSWERS, which represent the length of the shorter leg.
When the correct answer is plugged in, the area = 400.
B: 20
Longer leg = two more than three times the shorter leg = 2 + 3*20 = 62.
Area = (1/2)(20)(62) = 620.
Since the area is too great, a smaller answer choice is ...”

“Statement 1:
Test one case that also satisfies Statement 2.
Case 1: The frame is 8 inches tall, with the result that the total area of the frame and picture combined = 6*8 = 48
Area of the picture = (total area) - (shaded region) = 48-24 = 24.
Implication:
The width of the frame is 1 inch, ...”

“A general rule:
Given x^(even power) - y^(even power), where x and y are distinct positive integers, we can always simplify by applying the difference of two squares.
Each time we apply the difference of two squares to the expression in blue, the exponents are reduced by 1/2.
For example:
x⁸ - ...”

“For any evenly spaced set:
sum = (count)(median)
Sum of the first n even numbers = n * median of the first n even numbers
Sum of the last n odd numbers = n * median of the last n odd numbers
Since the ratio of the two sums = 16/85, we get:
(n * median of the first n even numbers) / (n * ...”

“Let Rex''s income = 100.
Since Quentin''s income is 60% less than Rex''s, Quentin''s income = 100 - (60% of 100) = 100-60 = 40.
Since Sam''s income is 25% less than Quentin''s, Sam''s income = 40 - (25% of 40) = 40-10 = 30.
After Rex gives 60% of his income to Sam, Sam''s new income = 30 + (60% ...”

“We can PLUG IN THE ANSWERS, which represent the value of x.
Since an absolute value cannot be equal to a negative value, the correct answer cannot be A or B.
D: x=2
If we plug x=2 into |x-6|=2x, we get:
|2-6| = 2*2
|-4| = 4
4 = 4.
Success!
The correct answer is D.”

“Let the distance between A and B = 120 miles.
Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles.
Since the average speed for the 120-mile leg between A and B = 60 mph, ...”

“The answer choices are already phrased as statements.
The OA is a statement that weakens the conclusion.
OA: Computer owners in the United States predominately belong to a demographic group that have long been known to spend less time watching television.
This statement indicates that a lack of ...”

“Let the distance between A and B = the LCM of the two speeds = 5*6 = 30 kilometers, implying that the distance for the entire round trip = 60 kilometers.
At a rate of 5 kph, the time to travel the 30 kilometers from A to B = d/r = 30/5 = 6 hours.
At a rate of 6 kph, the time to travel the entire ...”

“In ascending order of EMPLOYEES PER PROJECT, let the projects be numbered 1 through 100:
1, 2, 3.....49, 50, 51, ....98, 99, 100.
Projects 50 and 51 determine the MEDIAN number of employees:
Question rephrased: How many employees are assigned to PROJECTS 50 and 51?
Looking at the two ...”

“The sum for Lisa and Mike is 50 less than the sum for Norm and Mike.
Since Mike is common to both sums, the 50-photo difference must be yielded solely by Lisa and Norm.
Implication:
Lisa took 50 fewer photos than Norm.
We can PLUG IN THE ANSWERS, which represent the number of photos taken by ...”

“Circle ABCD:
The equation for a circle with a center at the origin and a radius of r is x² + y² = r².
The equation for circle ABCD is x² + y² = 5².
Thus, circle ABCD has a radius of 5.
Line EF:
3y = 4x + 25
y = (4/3)x + 25/3
Slope = 4/3.
A radius drawn to a point of tangency forms ...”

“In many cases, similar or identical solutions are posted when two experts respond at virtually the same time, with the result that the second poster is not aware of the first.
The time stamps for the two solutions here indicate that both solutions were posted at 11:45am.”

“The wording in Statement 1 does not convey a clear meaning:
For every value in the list, if the value is increased by 1, the number of distinct values in the list does not change.
Here, the term in red could convey to some test-takers that EVERY VALUE in the list is to be increased by 1.
Not the ...”

“Statement 1:
If profits increase by $X from the first year to the second year, then they must increase by $0 from the second year to the third year, with the result that the increase in profits from the first year to the third year (X+0 = $X) is the same as the increase in profits from the first ...”

“Statement 1:
25Q + 10D = 170
5Q + 2D = 34
To minimize the number of coins, we must maximize the value of Q.
If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34.
In this case, the total number of coins = 6+2 = 8.
If the value of Q decreases, then the total number of coins will ...”

“having + VERBed is a viable construction.
An introductory HAVING + VERBed modifier implies PRIOR ACTION: an action completed before the main verb.
HAVING FINISHED his dessert, John LEFT the table.
Here, HAVING FINISHED implies PRIOR ACTION -- an action completed before John LEFT the table.
...”

“Since 6% of the 1000-gallon tank is fluorine, the amount of fluorine = (6/100)(1000) = 60 gallons.
Since the total volume decreases at a rate of 10 gallons per day for 25 days, the decrease in the total volume = 10*25 = 250 gallons.
Remaining total volume = 1000-250 = 750 gallons.
Since 60 of the ...”

“CRITICAL POINTS in an equality occur when the two sides are EQUAL or the inequality is undefined.
Here, the two statements provide the critical points for the inequality in the prompt:
When x=0, the two sides are equal.
When x=1, the inequality is undefined.
To determine the range(s) where the ...”

“Statement 1:
For every $100 commission that Dan earns, Jeff earns $120 in commission.
Since the commission rates for Dan and Jeff are unknown, no way to determine whether Jeff recorded more sales revenue than Dan.
INSUFFICIENT.
Statement 2:
Since Jeff''s sales and Dan''s sales can be any ...”

“Let a=b=0.5, implying that the rectangle''s length = a+b = 0.5+0.5 = 1 and that its area = (1/0.5) + (1/0.5) = (10/5) + (10/5) = 2+2 = 4.
Since the rectangle has an area of 4 and a length of 1, its width = 4.
The correct answer must yield a value of 4 when a=b=0.5.
Only E works:
1/ab = 1/(0.5 * ...”

“N/J = 134.08 = 13408/100 = 3352/25.
The resulting ratio indicates that N must be multiple of 3352 and that J must be a multiple of 25.
Of the five answer choices, only E is a multiple of 25.
The correct answer is E.”

“We can PLUG IN THE ANSWERS, which represent the number of blue marbles in the second container.
When the correct answer is plugged in, the probability of selecting 2 red marbles OR 2 blue marbles = 1/2.
B: 4 blue marbles, implying a total of 10 marbles in the second container
Case1: 2 red ...”

“=
We can PLUG IN THE ANSWERS, which represent the number of tulips.
When the correct answer is plugged in, the total cost = $48.
D: 24 tulips, implying 16 roses, for a total of 40 flowers
Since each of the 24 tulips costs $1, and each of the 16 roses costs $1.50, we get:
Total cost = (24*1) ...”

“Let r=100 cents.
For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars.
Let x = 2 miles.
Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars.
With a 50% discount, the cost in dollars = 3. This is the target.
Plug x=2 and r=100 into the answers to see which yields the ...”

“We can PLUG IN THE ANSWERS, which represent the length.
When the correct answer is plugged in, perimeter = 360.
B: 140
Since the length is twice the width, W = 70, with the result that the perimeter = 140+140+70+70 = 420.
Since the perimeter is too great, a SMALLER answer choice is needed.
...”

“Generally, a COMMA + VERBing modifier serves to modify the nearest preceding action and the agent of this action.
C: instructions that...will help merchants confirm a check''s authenticity, by including reminders to watch the endorsement.
.Here, COMMA + by including seems to modify merchants ...”

“When a positive integer is divided by 100, the remainder is yielded by the last two digits:
123/100 = 1 R23
548/100 = 5 R48
692/100 = 6 R92
Thus:
The remainder when 7¹⁰ is divided by 100 is equal to the last two digits of 7¹⁰.
Calculate the last two digits for consecutive powers of 7 ...”

“TIME and RATE have a reciprocal relationship.
Statement 1:
The time ratio for Barbara and Alice = (14 hours)/(21 hours).
The rate ratio for Barbara and Alice is equal to the reciprocal of the time ratio:
(B''s rate)/(A''s rate) = 21/14 = 3/2.
Let B = 3 units per hour and A = 2 units per ...”

“Let James'' rate = 3 mph.
James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James ...”

“Each of the 10 members has an EQUAL chance of being elected secretary.
P(Harry is elected secretary) = 1/10.
Each of the 10 members has an EQUAL chance of being elected treasurer.
P(Harry is elected treasurer) = 1/10.
Since EITHER outcome is favorable, we ADD the fractions:
1/10 + 1/10 = 2/10 = ...”

“The conclusion is constrained to the case at hand:
Of the 10 babies recently placed with parents, 8 were given to friends of the staff.
The assumption is that the premise (the parents given babies -- including the 8 friends --all far surpassed the agency''s criteria) is sufficient to prove the ...”

“Let:
b = the number of boys
g = the number of girls
s = the number of cents for each soda
j = the number of cents for each juice box
Note:
All of the values above must be POSITIVE INTEGERS.
Case One: If every boy in a kindergarten class buys a soda and every girl in the same class buys a ...”

“Let X = the number of 52¢ lemonades and Y = the number of 58¢ lemonades.
Since the question stem asks for the number of 52¢ lemonades, we get:
What is the value of X?
Statement 1:
X+Y = 9
Since X can be any value between 0 and 9, inclusive, INSUFFICIENT.
Statement 2:
52X + 58Y = 492
...”

“Alternate approach:
The 3 red cars must occupy a combination of 3 spaces.
From 5 spaces, the number of ways to choose a combination of 3 for the red cars = 5C3 = (5*4*3)/(3*2*1) = 10.
Number of options for the blue car = 2. (Either of the 2 remaining spaces.)
Number of options for the yellow ...”

“Premise:
All of the applicants given babies far surpassed the adoption criteria.
Conclusion:
In placing 8 of the 10 babies with friends, the staff was not guilty of favoritism.
Apply the NEGATION TEST.
When the correct answer is negated, the conclusion will be invalidated.
B, negated:
Of ...”

“In other words:
How many ways can 5 girls and 5 guys be divided into pairs, if each pair must consist of one girl and one guy?
Number of options for the first girl = 5. (Any of the 5 guys.)
Number of options for the second girl = 4. (Any of the 4 remaining guys).
Number of options for the ...”

“The average of s and 10 lies HALFWAY between s and 10 on the number line:
s------------AVERAGE------------10
Statement 1:
Since t closer to 10 than to s, t must be greater than the average of s and 10, as shown here:
s-----------AVERAGE---t----------10
Thus, the answer to the question stem is ...”

“Good committees = total committees - bad committees.
Total committees:
From 10 people, the number of ways to choose 4 = 10C4 = (10*9*8*7)/(4*3*2*1) = 210.
Bad committees:
Since a good committee includes at most 1 married couple, a bad committee is composed of 2 married couples.
From 3 ...”

“For any evenly spaced set:
sum = (number)(median)
We can PLUG IN THE ANSWERS, which represent the sum.
Since the number of integers can be 5 or 7, the sum must be a multiple of both 5 and 7.
Eliminate A, which is not divisible by 5.
Eliminate D, which is not divisible by 7.
The equation in ...”

“THE INSURED is the person covered by the insurance.
Plan A:
If $1000 is LESS than 50% of the cost level, then THE INSURED pays $1000, and PLAN A pays the remainder.
If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and PLAN A pays the remainder.
Plan ...”

“Statement 1 indicates that 80 grams of water are added to the 80 grams of original solution, DOUBLING the total volume from 80 grams to 160 grams
Statement 2 indicates that the added water reduces the acid concentration by 1/2.
Doubling the total volume will reduce the acid concentration by 1/2 ...”

“We can PLUG IN THE ANSWERS, which represent the original number of trees.
Since the number of trees increases by 1/4 each year, the correct answer must be a multiple of 4.
The last 2 digits of a multiple of 4 must themselves form a multiple of 4.
Eliminate A (1250) and C (2250), since 50 is ...”

“Case 1:
Every 6-block rectangle with a base of 2 and a height of 3 yields 4 possible L-shapes:
https://i.postimg.cc/1gJCfb5J/chessboard_L_shape_1.png
Chessboard:
https://i.postimg.cc/LYJThXW8/chessboard_whole.png
The base for the 6-block rectangle shown above can appear in rows 1 through 6, ...”

“During each of Amit''s 4 shifts, he paints 1/2 of the room, leaving 1/2 the room unpainted.
Since 1/2 of the room is left unpainted FOUR TIMES, the total fraction left unpainted as a result of Amit''s 4 shifts = (1/2)⁴.
Since Ian works after each of Amit''s first 3 shifts, Ian paints a total ...”

“Since the answer choices are in terms of a variable -- the value of r -- we can PLUG IN.
Let the ENTIRE WIRE be used to form the square.
Then:
Perimeter of the square = 40.
Side = 10.
Area = 100.
Circle area + square area = 0 + 100 = 100. This is our target.
Since the circle has no ...”

“x²y² will be even unless both x and y are ODD.
Question stem, rephrased:
Are x and y both odd?
Statement 1:
x+5 is prime number greater than 2 and thus must be ODD.
Implication:
x+5 = ODD
x = ODD - 5 = ODD - ODD = EVEN.
Since x is even, x and y cannot both be odd.
SUFFICIENT.
...”

“Rate and time have a RECIPROCAL RELATIONSHIP.
The RATE RATIO for the hiker and cyclist = 4 mph : 20 mph = 1:5.
Thus:
The TIME RATIO for the hiker and cyclist = the reciprocal of the rate ratio = 5:1.
Implication:
The hiker will take 5 TIMES AS LONG as the cyclist to travel the same ...”

“Alcohol percentage in the original solution: 3%.
Alcohol percentage in the added water: 0%.
Alcohol percentage in the mixture: 1%.
Let S = the original solution and W = the added water.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: ...”

“When the same distance is traveled at two different speeds, the average speed for the entire trip will be a bit LESS than the average of the two speeds.
Since (70+50)/2 = 60, the average speed for Vivian''s''s entire trip must be a bit less than 60.
The correct answer is B.”

“An alternate approach is to PLUG IN THE ANSWERS, which represents Tom''s current age.
When the correct answer is plugged in, Mom''s age in 6 years will be 3 times Tom''s age in 6 years.
D: Tom = 6
Since Mom is currently 5 times as old as Tom, Mom = 5*6 = 30.
Tom''s age in 6 years = 6+6 = 12.
...”

“First 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19.
The sum will be even if 2 is among the three numbers selected, with the result that the sum = EVEN PRIME + ODD PRIME + ODD PRIME = EVEN.
Since 3 NUMBERS are selected from 8 OPTIONS, the probability that 2 will be among the three numbers selected = ...”

“Let T = the total number of employees.
Since 60% of the employees are over 40, we get:
Over 40 = 0.6T
30% of those over 40 -- in other words, 30% of the expression in blue -- have master''s degrees.
Thus:
Over 40 with master''s = 0.3(0.6T).
To calculate the value of the expression in ...”

“Since Pat travels at 30 miles per hour for the first 12 minutes -- the equivalent of 1/5 hour -- the distance traveled in the first 12 minutes = (30)(1/5) = 6 miles.
Since the remaining 14 miles are traveled at 8 miles per hour, the time to travel the remaining 14 miles = 14/8 = 7/4 hours = 1 hour ...”

“The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3.
Draw a VENN DIGRAM showing where the prime factors of n, 16 and 45 overlap:
https://i.postimg.cc/xkyNCFg7/GCF_Venn_n_16_and_45.jpg
The diagram implies the following:
Since n and ...”

“Good arrangements = total arrangements - bad arrangements.
Total arrangements:
Number of ways to arrange 5 elements = 5!.
But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED.
The reason:
When the ...”

“Let the total number of students = 100.
Since 50% of the students study science, the number of science students = (50/100)(100) = 50, implying that the number of non-science students = 100-50 = 50.
Since 30% of the 50 science students score more than 80%, the number of science students who ...”

“5-pound bags = ($13.85)/5 ≈ $3 per pound.
10-pound bags = ($20.43)/10 = more than $2 per pound.
25-pound bags = ($32.25)/25 = less than $1.50 per pound.
To minimize the cost, we must maximize the number of 25-pound bags, which offer seed at the lowest price per pound.
Two 25-pound bags = 50 ...”

“ALWAYS KEEP YOUR EYES ON THE ANSWER CHOICES.
C, D and E imply that the flower bed is probably a 6-8-10 triangle in which y=6, x = y+2 = 6+2 = 8, and z=10.
Check whether this triangle satisfies the condition that the flower bed has an area of 24 square yards:
Area of a 6-8-10 triangle = ...”

“Let the total number of chocolates = the LCM of the four denominators 2, 5, 6 and 12 = 60.
Number of chocolates given to the four children:
(1/2)(60) = 30
(1/5)(60) = 12
(1/6)(60) = 10
(1/12)(60) = 5
Total number of chocolates = 30+12+10+5 = 57.
The correct answer is C.”

“Of the units sold, non-condos constitute 85% = 85/100 = 17/20.
Implication:
Of every 20 units sold, 17 are non-condos, with the result that the number of non-condos must be a multiple of 17.
A. 16000
B. 13600
C. 12400
D. 11200
E. 8600
Only the portion in green is a multiple of 17:
...”

“Let G = at least 3 goals and NG = not at least 3 goals.
Let W = win the match and NW = not win the match.
Use a DOUBLE-MATRIX to organize the data:
https://i.postimg.cc/JHLj6Tyr/matrix_goals_wins_0.png
The probability that Ronaldo will score at least 3 goals in the match is 0.59.
The ...”

“Let S = the smallest number of L = the largest number.
Since the largest number is 4 more than 3 times the smallest number, we get:
L = 3S + 4
L-4 = 3S
(L-4)/3 = S.
Since the average is 50 -- and the numbers are not all the same -- S must be LESS THAN 50, while L must be greater than 50.
...”

“Once the child has been placed at the table:
Number of ways to arrange the 2 women in the 2 seats adjacent to the child = 2! = 2.
Number of ways to arrange the 4 men in the remaining 4 seats = 4! = 24.
To combine these options, we multiply:
2*24 = 48.
The correct answer is C.”

“Number of digit options for the repeated digit = 9. (Any digit but 0.)
Number of digit options for the non-repeated digit = 8. (Any digit but 0 and the digit already used.)
Number of position options for the non-repeated digit = 3. (The hundreds place, the tens place, or the units place.)
To ...”

“Algebra:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates.
(A+B)(3) = 1 widget.
If Machine A''s speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates.
(2A+B)(2) = 1 widget.
...”

“We can PLUG IN THE ANSWERS, which represent A''s time to produce 1 widget.
Since A and B working together take 3 hours to produce 1 widget, A working alone must take MORE than 3 hours.
Eliminate A, B and C.
Let the value of each widget = 30 units.
Since A and B together take 3 hours to produce ...”

“Use a DOUBLE-MATRIX to organize the data.
Statements combined:
Case 1: m=25% and c=25%
Total number of males = (25/100)(120) = 30.
Total number of custodial employees = (25/100)(120) = 30.
The following matrix is yielded:
https://i.postimg.cc/H88Lq5zN/matrix_custodial_1.png
In this case, ...”

“The default referent for a subject pronoun is the subject of the preceding INDEPENDENT CLAUSE.
A: Those who have public pensions are being pursued strongly by pension advance companies that operate without much oversight from banking regulators, but they are now drawing scrutiny.
Here, the default ...”

“This interpretation is not valid.
The comparative in blue is clearly an ADJECTIVE describing a city..
Since as big as refers not to China but to A CITY. no comparison between China and Singapore is implied.
The sentence unambiguously compares A CITY to Singapore, as discussed below.
...”

“Almost no math is needed here.
Answer choice A implies the following:
BCD is a 45-45-90 triangle in which each leg has a length of 1.
DEF is a 45-45-90 triangle in which each leg has a length of 5.
Answer choice E implies the following:
BCD is a 45-45-90 triangle in which each leg has a ...”

“In four years, Andy will be twice as old as Betsy.
Since Andy''s age in 4 years is twice Betsy''s age in 4 years, we get:
A+4 = 2(B+4)
A+4 = 2B+8
A-2B = 4.
Statement 1:
Since Andy''s age 4 years ago is twice Betsy''s current age, we get:
A-4 = 2B
A-2B = 4.
Same equation as given in the ...”

“Since 1000 - 101 ≈ 900 -- and the answer choices are a bit spread out -- we can count the multiples of 33 simply by dividing 33 into 900:
900/33 = 300/11 = a bit more than 27.
Thus, there are 27 multiples of 33 between 101 and 1000.
The correct answer is B.”

“OA: A neutron star, as small as 12 miles in diameter but containing half as much matter as the Sun, has a gravitational force at its surface about 67 billion times greater than that on Earth.
The green portion conveys the following meaning:
The words in brackets are omitted so that the green ...”

“I believe that the problem has been transcribed incorrectly.
Statement 1 should indicate that Rasheed bought not 2 fewer packages but only 1 fewer package, as shown in the following screen shot:
https://i.postimg.cc/t7bcm77Z/rasheed_Gprep-ds-2.jpg
If we know the number of chocolate BARS that ...”

“In the number line shown, the distance between 0 and a, a and b, and a and c is in the ratio of 1:2:3.
To determine the ratio of a to b to c, TEST AN EASY CASE.
Let a=1.
Since a is ONE PLACE to the right of 0, b must be TWO PLACES to the right of a (implying that b=3), while c must be THREE ...”

“Let M = the rate for each man and W = the rate for each woman.
The TIME RATIO for 12 men and 16 women to 13 men and 24 women is 5 days to 4 days.
Since time and rate are RECIPROCALS, the RATE RATIO for 12M+16W and 13M+24W is equal to the reciprocal of the time ratio:
(12M+16W)/(13M+24W) = ...”

“When a value increases repeatedly by r%:
Final amount = Original amount * (1 + r/100)^number of changes.
Let original amount = 1.
Since the original amount increases by a factor of 16:
Final amount = 16.
Since the investment increases by 2% every quarter:
r = 2.
Since x = the number of ...”

“We can PLUG IN THE ANSWERS, which represent the amount of cider.
When the correct answer is plugged in, the amount of alcohol in the 750 ml bottle = 87 ml.
Since the alcohol percentage in the cider = 5% = 1/20, the correct answer is almost
certain to be a multiple of 20.
Of the five answer ...”

“Average = sum/quantity.
In this case:
Average speed = (sum of the minutes spent at each speed)/(total number of minutes).
Total time spent at 15mph = 30 minutes.
Total time spent delivering pizzas at 0mph = 30 minutes.
Total time spent at 30mph = 15 minutes.
Average speed = (15*30 + 0*30 + ...”

“P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).
P(1st apple is not spoiled) = 4/5. (Of the 5 apples, 4 are not spoiled).
P(2nd apple is not spoiled) = 3/4. (Of the 4 remaining apples, 3 are not spoiled).
Since we want both events to happen, we multiply the fractions:
...”

“Statements combined:
Each statement conveys the same information: that the average speed for the whole trip was 5 miles per hour.
The AVERAGE speed for the whole trip does not constrain the speed AT THE HALWAY POINT.
At the halfway point, the speed could be ANY NONNEGATIVE VALUE.
Thus, the ...”

“The answer choices represent the ratio between the numerator and the denominator of the given expression.
Option A implies that the numerator is about 14 times the denominator
Option B implies that the numerator is less than 7 times the denominator.
Option C implies that the numerator is 41 times ...”

“Since the answer choices are very spread out, we can BALLPARK -- and we can be somewhat lax with our estimations.
Numerator:
If the 11 greatest terms were 10²=100, the sum of the 11 greatest terms = 11*100 = 1100.
If the 11 greatest terms were 20²=400, the sum of the 11 greatest terms = ...”

“The sum of the 3 angles of a triangle = 180.
The sum of the parts of the ratio = 3+4+5 = 12.
Since 180/12 = 15, the multiplier for the ratio is 15, implying that the largest angle = 5*15 = 75.
The correct answer is D.”

“Statement 1:
Case 1: 1 sweater is sold for $270
Case 2: 3 sweaters are sold for $90 each
Since the number of sweaters sold can be different values, INSUFFICIENT.
Statement 2:
Since the $30 markup is 1/2 the cost of each sweater, the cost of each sweater = 60.
Thus, the selling price of ...”

“The GRE is administered by ETS, which also used to administer the GMAT.
The GRE Quantitative Guide states that any side of a triangle or parallelogram can be used as a base.
The GMAT is likely to abide by this definition.
But the terms length and long seem to connote a different meaning when ...”

“Since Doris is 12 years older than Fred, let Fred = 2 and Doris = 2+12 = 14.
y = sum of their ages = 2+14 = 16.
Since Fred = 2 and y=16, Fred''s age y years from now = 2+16 = 18. This is our target.
Now plug y=16 into the answers to see which yields the target value of 18.
Only D works:
3y/2 - ...”

“The trick is translate the chemical relationship into the following equation:
R = A²/B
Here''s why the equation above works:
1)The problem states that R is directly proportional to A². Directly proportional means that as one value increases, the other value also increases by a ...”

“Of the 50 fish caught in the second catch, 2 were tagged:
2/50 = 4/100 = 4%.
Since the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, the total number of tagged fish -- 50 -- must be equal to about 4% of the total number of fish in the pond:
50 = ...”

“Since m=2 will yield an integer value for the given expression and will make the math easier, ignore the condition that m>2 and let m=2.
Plugging m=2 into 5^(m-2) * 2^(m+2), we get:
5⁰2⁴ = 1*16 = 16.
Since the result is a 2-digit integer, n=2.
The correct answer must work for n=m=2.
Only ...”

“Let the rate for each man = 1 widget per day, implying that the rate for 24 men = 24 widgets per day.
Since 24 men complete the job in 16 days, the total amount of work = rt = 24*16 widgets.
Since 32 women require 24 days, the rate for 32 women = w/t = (24*16)/24 = 16 widgets per day.
Since ...”

“Given that the answers choices are integers, I believe that the following reflects the problem''s intent:
The three fractions in the prompt -- 1/4, 1/3 and 1/2 -- imply that the fine must be divisible by 4, 3 and 2.
Smallest possible case:
Total fine = 4*3*2 = 24.
Since Sam paid $4 less ...”

“Option B for SC18 in the OG12:
Plants are more efficient at acquiring carbon than fungi.
Logical interpretation 1:
Plants are more efficient at acquiring carbon than
Logical interpretation 2:
Plants are more efficient at acquiring carbon than fungi
Since B allows for more than one logical ...”

“The alarm sounds for 3 of EVERY 4 BEARS that actually appear,
If 4 bears appear, then the number of alarms = 3.
Since the alarm sounds only 3 times for 4 bears, 1 of these 4 bears is undetected.
Since there are 10 false alarms for every 1 undetected bear, the number of false alarms = 10.
Thus, ...”

“The answer choices represent the price per pound:
(total cost)/(total number of pounds).
Since 7 pounds are purchased, the correct answer must have a denominator of 7.
A, C and D lack denominators and thus can be eliminated.
Since the denominator in B does not have to be 7, eliminate B.
The ...”

“Statement 1:
Time and rate have a RECIPROCAL relationship.
3 TIMES AS FAST implies 1/3 THE TIME.
Thus, the 2 hours that would be spent traveling 3 times as fast must be equal to 1/3 the actual time:
2 = (1/3)t
t = 6 hours.
SUFFICIENT.
Statement 2:
Here, the time can be any nonnegative ...”

“Number of options for the units digit = 5. (1, 3, 5, 7, or 9.)
Number of options for the thousands digit = 1. (Must be the same as the units digit.)
Number of options for the hundreds digit = 10. (Any of the digits 0-9.)
Number of options for the tens digit = 1. (Must be the same as the hundreds ...”

“Original ratio:
Let the original price = 1 and the original earnings = 1.
Resulting ratio:
price/earnings = 1/1 = 1.
New ratio:
Let k=200 and m=100.
Since the price increases by k=200%, the new price = 1 + (200/100)(1) = 3.
Since the earnings increase by m=100%, the new earnings = ...”

“For any quadratic in the form x² + bx + c = 0:
Sum of the roots = -b.
Product of the roots = c.
In the given quadratic, b = -40.
Thus, the sum of the roots = -b = -(-40) = 40.
The correct answer is D.”

“Since 4, 14 and 27 are all factors of n, the prime-factorization of n must include 2*2, 2*7 and 3*3*3.
n = r³ implies that n is a perfect cube.
The prime-factorization of a perfect cube must include at least 3 of each prime factor.
Thus, the prime-factorization of n must include at least three ...”

“When the same distance is traveled at two different speeds, the average speed will be the same for ANY DISTANCE.
Thus, we can solve the problem above using a distance that is divisible by the two speeds.
Let the distance in each direction = 30 miles.
Time to run 30 miles at a rate of 10 miles per ...”

“Mr. Smith shook hands with 3 times as many men as women.
The phrase in blue implies that the number of men who shook hands with Mr. Smith is a MULTIPLE OF 3.
Thus, the total number of men = (multiple of 3) + (Mr. Smith).
In math terms:
Number of men = 3a + 1, where a is a positive integer.
...”

“A comparison is questionable if it allows for more than one logical interpretation.
Case 2 is not a logical interpretation of your revision of E.
No reader will construe that what MANAGERS find is being compared to what A GRASPING finds.
Since only Case 1 constitutes a logical interpretation, the ...”

“Since the graph intercepts the x-axis to the left of the y-axis and has only one solution, its graph is as follows:
y = (x-k)², where k<0.
The equation above has an x-intercept at (k, 0), as shown in the figure above.
The answer choices represent the sum of k (the x-intercept) and p (the ...”

“Alternate approach:
Number of options for A = 6. (Any of the 6 chairs.)
Number of options for B = 5. (Any of the 5 remaining chairs.)
Number of options for C = 4. (Any of the 4 remaining chairs.)
Number of options for D = 3. (Any of the 3 remaining chairs.)
Number of options for E and F = 1. ...”

“Let the rate for the fastest machine = 5 units per hour and the rate for the slowest machine = 1 unit per hour.
Since the fastest machine works at a rate of 5 units per hour for all 9 hours, the work produced by the fastest machine = rt = 5*9 = 45 units.
Since the slowest machine works at a rate ...”

“If we use 0 as a placeholder -- so that 007 represents 7, 072 represents 72, etc. -- then we need to count the number of times that 7 will appear among the 3-digit integers from 000 to 999, inclusive.
Total number of 3-digit integers from 000 to 999, inclusive = biggest - smallest + 1 = ...”

“Alternate approach:
x² + 3x = 10-k
x² + 3x = constant.
Since x=4 and the correct answer choice are both roots, they must yield the same result when plugged into x² + 3x.
Plugging x=4 into x² + 3x, we get:
4² + 3*4 = 28.
If we test the answer choices, only x=-7 yields the same result ...”

“Alternate approach:
Since Science class must be followed immediately by Science lab, Science class cannot be taken during the last period.
Thus:
Number of options for Science class = 4. (Any of the first 4 periods.)
Number of options for Science lab = 1. (Must be the period immediately after ...”

“15 matched pairs = 30 socks.
E: 12
If Angela has 12 matched pairs left -- for a total of 24 socks -- then the number of socks lost = 30-24 = 6.
Not viable, since Angela must lose 7 socks.
The correct answer is E.”

“Plug in easy numbers for the two rates.
Then plug in a distance that is a multiple of both the two individual rates and the COMBINED rate.
Let the high speed rate = 3 miles per hour.
Let the regular rate = 2 miles per hour.
Combined rate for the trains = 2+3 = 5 miles per hour.
Let z = ...”

“a phenomenon that is caused by human beings.
Here, the that-clause in green serves to modify a phenomenon.
Question: What KIND of phenomenon?
Answer: A phenomenon THAT IS CAUSED BY HUMAN BEINGS.
Most scientists agree that the statement above is true.
To convey this meaning, we insert most ...”

“Incorrect:
When compared with most sport utility vehicles, minivans get better gas mileage.
Here, the usage of when compared is unwarranted and conveys a nonsensical meaning, implying that minivans GET better mileage at the same time as they are COMPARED.
The following is sufficient to convey the ...”

“How many ways can the letters BBBGG be arranged?
Number of ways to arrange 5 elements = 5!.
But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED.
The reason:
When the identical elements swap positions, the ...”

“There are 6 positions in the integer.
The two 4''s must occupy a pair of positions.
From the 6 positions, the number of ways to choose a pair for the two 4''s = 6C2 = (6*5)/(2*1) = 15.
The remaining 4 positions must be occupied by 3, 5, 7 or 8, 7 or 8.
Number of options for the 3 = 4. (Any ...”

“We can PLUG IN THE ANSWERS, which represent the original price of the item.
When the correct answer is plugged in, George reimburses the store $40.50.
Since the coupon discount = 15% = 15/100 = 3/20, the original price of the item is almost certainly a multiple of 20.
Of the 5 answer choices, ...”

“We can PLUG IN THE ANSWERS, which represent the daughter''s current age.
When the correct answer is plugged in, the nd the dau
B: 10, implying that the daughter''s age 8 years ago = 10-8 = 2
Since the son 8 years ago was twice as old as the daughter, the son''s age 8 years ago = 2*2 = 4, ...”

“Translate the words into math.
The DISTANCE between x and 0 is |x|.
HALFWAY between two numbers is the AVERAGE of the two numbers.
Statement 1: The distance between r and 0 is 3 times the distance between m and 0.
|r| = 3|m|
r = 3m or r=-3m.
No way to solve for r.
INSUFFICIENT.
...”

“Clearly, neither statement is sufficient on its own.
Statements combined:
The statements indicate that a and b are CONSECUTIVE PERFECT CUBES.
Make a list of perfect cubes:
1, 8, 27, 64, 125...
Calculating the difference between one perfect cube and the next, we get:
8-1 = 7
27-8 = 19
...”

“Let the amount saved each month = $1.
Total saved for the entire year = 12*1 = $12.
Since the total saved for the entire year -- $12 -- is 3 times the total not saved each month, the total not saved each month = 12/3 = $4.
Thus, the total monthly pay = (total saved each month) + (total not saved ...”

“We can PLUG IN THE ANSWERS, which represent the amount of Y.
Since the percentage for the mixture (35%) is closer to Y''s percentage (30%) than to X''s percentage (50%), Y must constitute MORE THAN 1/2 of the 16-liter mixture.
Thus, the amount of Y must be equal to more than 8 liters.
Eliminate ...”

“Since the cucumbers are 99% water, the 100 pounds of cucumbers are composed of 99 pounds of water and 1 POUND OF OTHER STUFF.
After evaporation makes the cucumbers 98% water, the 1 POUND OF OTHER STUFF must constitute 2% of the new total:
1 = (2/100)x
x = 100/2 = 50.
The correct answer ...”

“Statement 1:
(women for X) : (women against X) = 2:1.
Of every 3 women voters, 2 voted for X, while 1 voted against X.
In other words, 2/3 of women voters voted for X.
No way to determine the NUMBER of women who voted for X.
INSUFFICIENT.
Statement 2:
No info about women voters.
...”

“Substituting n= 10¹⁰ into n^n = 10^d, we get:
(10¹⁰ )^(10¹⁰)= 10^d
When an exponent is raised to a power, we MULTIPLY the exponents.
Multiplying the exponents in blue, we get:
10^(10*10¹⁰) = 10^d
10^(10¹¹) = 10^d
Since each side has the same base, the exponent in blue must be ...”

“For the 5-digit integer to be a multiple of 4, the last two digits must form a multiple of 4.
Options:
04, 12, 20, 24, 32, 40, 52.
Case 1: Last 2 digits include 0
Number options for the last 2 digits = 3. (04, 20 or 40.)
Number of options for the ten-thousands place = 4. (Any of the 4 ...”

“In deference to Brent''s concerns, the problem should read as follows:
x miles north, y miles east, and z miles in a straight line back to x constitute a right triangle with legs x and y and hypotenuse z.
The only right triangle in which all 3 sides are integers and the shortest leg is 5 is ...”

“Sum = (quantity)(average).
The average (arithmetic mean) of the five numbers in a data set is 72.
Sum = 5*72 = integer with a UNITS DIGIT OF 0.
The average (arithmetic mean) of the first three numbers is 98.
Sum = 3*98 = integer with a UNITS DIGIT OF 4.
For the sum of all 5 numbers to ...”

“Let the pay rate = $1 per hour.
Let Angela''s time = 4 hours.
Since Linda works 50% longer, Linda''s time = 4 + (1/2)4 = 6 hours.
Since a total of 10 hours are worked at a rate of $1 per hour, the total pay = 10*1 = $10.
Since each worker receives m dollars of the total pay, m=$5.
Since ...”

“An alternate approach is to PLUG IN THE ANSWERS.
When the correct answer is plugged in, the two companies will charge the same amount.
B: 10 minutes
Since United charges $10 plus $0.25 per minute, the charge from United = 10 + 10(0.25) = $12.50.
Since Atlantic charges $12 plus $0.20 per ...”

“We can PLUG IN THE ANSWERS.
To yield a remainder of 1 when divided by 4, the correct answer must be 1 more than a multiple of 4.
The smallest answer choice that is 1 more than a multiple of 4 is 61.
When 61 is divided by 2, 3 or 5, the remainder is 1 in each case.
The correct answer is C.”

“One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time.
Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 ...”

“The OA implies the following:
The cost of running nuclear power plants is about the same as for other types of power plants.
The prepositions phrase in blue serves the same function as the prepositional phrase in red: both serve to modify the cost.”

“to run for X implies that X is a GOAL.
Mary plans to run for president.
Conveyed meaning:
The office of president = Mary''s goal.
Thus, to run for other types of power plants implies that OTHER TYPES OF POWER PLANTS constitute a goal.
Not the intended meaning.
No one is attempting to reach ...”

“OA: The cost of running nuclear power plants is about the same as for other types of power plants.
Since the blue portion provides its own referent (other types of power plants), the referent in the red portion (nuclear power plants) is not implied in the blue portion.
C: It costs about the ...”

“To count the positive factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)...
Generally, GMAT problems about factors are constrained to POSITIVE factors.
On the GMAT, the posted ...”

“Time and rate have a RECIPROCAL RELATIONSHIP.
If Mary works TWICE as fast as John, Mary''s time will be 1/2 John''s time.
If Mary works THREE TIMES as fast as John, Mary''s time will be 1/3 John''s time
Since 4 machines will work 4 times as fast as 1 machine, the time for 4 machines will ...”

“Another approach:
10¹¹ (100,000,000,000) is 100 TIMES the value of 10⁹ (1,000,000,000).
Implication:
11¹¹ must be MORE THAN 100 TIMES the value of 9⁹.
Since 9⁹ is so small when compared to 11¹¹, we can ignore the value of 9⁹ when we approximate:
11¹¹ - 9⁹ ≈ 11¹¹
The ...”

“One approach is to use the following equation:
Total = Group 1 + Group 2 - Both + Neither
The big idea is to SUBTRACT THE OVERLAP.
In the problem above, there is an overlap between the applicants with at least 4 years'' experience and the applicants with degrees.
Some applicants belong to BOTH ...”

“Every answer choice includes at least one negative sign.
Test coordinate pairs that include at least one negative value.
Case 1: a=1 and b=-1, so that (a, b) = (1, -1)
Plug a=1 and b=-1 into the answer choices to see whether one of the answer choices yields a point in the same quadrant as ...”

“Statement 1:
Make a list of options for z/2:
z/2 = 0, 2, 4, 6, 8...
To get a list of options for z, multiply every value by 2:
z = 0, 4, 8, 12, 16...
In every case, z is an even integer, so the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
Make a list of options for 3z:
3z ...”

“It is not possible for the two products -- that of the two chosen numbers and that of the two unchosen numbers -- to be equal.
Each of the two products has the same probability of being greater.
Thus, the probability that the product of the two chosen numbers is greater = 1/2.
The correct ...”

“In ascending order, let the 5 trophy values be a, b, c, d and e.
To maximize the value of d -- the second highest value -- we must MINIMIZE the values of a, b and c.
Since every child must have a different number of trophies, the least possible values for a, b and c are a=1, b=2, and c=3.
Since ...”

“We can PLUG IN THE ANSWERS, which represent the total number of notes.
The number of €10 notes they take is double the number of $10 notes they take.
Thus, the ratio of €10 notes to $10 notes = 2:1.
Since the sum of the parts of this ratio = 2+1 = 3, the total number of notes must be a ...”

“P(sibling pair) = (total number of sibling pairs)/(total number of possible pairs).
Total number of possible pairs:
There are 1000 juniors and 800 seniors.
Total number of ways to combine 1 junior with 1 senior = 1000*800 = 800,000.
Total number of sibling pairs = 60.
Thus:
...”

“Statement 1:
Make a list of options for 5n:
5n = 1, 2, 3, 4, 5...
To get a list options for n, divide every value above by 5:
n = 1/5, 2/5, 3/5, 4/5, 1...
If n = 1/5, the answer to the question stem is NO.
If n = 1, the answer to the question stem is YES.
INSUFFICIENT.
Statement 2:
Make a ...”

“The company requested 3 more 2¢ envelopes than 5¢ envelopes.
Let the number of 5¢ envelopes = 2, and the number of number of 2¢ envelopes = 2+3 = 5, with the result that the cost of the envelopes = (5*2) + .(2*5) = 20 cents.
A company hired a printer to produce a total of x + 1 envelopes.
...”

“There are twice as many strawberry candies as grape candies.
If G=1, then S=2.
There are twice as many apple candies as strawberry candies.
If S=2, then A=4.
There are twice as many apple candies as orange candies.
If A=4, then O=2.
Resulting ratio:
G:S:A:O = 1:2:4:2.
Since the sum of the ...”

“When we count the total in Science, the total in Drama, and the total in Band, any students in exactly two of the clubs are counted TWICE.
Thus, we must SUBTRACT these students so that they are not double counted:
Total = Science + Drama + Band - (exactly 2 clubs) = 20 + 30 + 12 - (8+6+4) = 44.
...”

“Put the ranges over the same DENOMINATOR:
A: 0 and 3/20
B. 30/20 and 1/5 -- 3/20 and 4/20
C. 1/5 and 1/4 --> 4/20 and 5/20
D. 1/4 and 3/10 --> 5/20 and 6/20
E. 3/10 and 1/2 --> 6/20 and 10/20
Since the greatest range is offered by E (10/20 - 6/20 = 4/20), the number is most likely ...”

“E, rephrased as a basic statement:
The other species on which deer tick larvae feed harbor other bacteria that ticks transmit to humans.
The conclusion is constrained to the number of ticks infected with the bacterium that causes LYME DISEASE.
Information about other bacteria is irrelevant ...”

“Alternate approach:
To earn exactly $100 in interest at rate of $15 earned each month, the number of months required = 100/15 = 20/3 = 6.66 months.
The smallest integer greater than 6.66 is 7.
Implication:
After 7 months, the total amount of interest will for the first time EXCEED $100, with ...”

“Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them.
Since Stacy is 1/4 faster than Katie, for every 4 miles that Katie travels, the distance traveled by Stacy = 4 + (1/4)(4) = 5 miles.
Thus, of every 9 miles traveled when Stacy and Katie work ...”

“Sum of the 10 terms = (quantity)(average) = 10*999 = 9990.
If we add the units digits of the nine given terms, we get:
3+4+6+7+8+1+1+2+4 = 36.
The sum of the nine given terms has a units digit of 6.
The sum of all ten terms has a units digit of 0.
Since (units digit of 6) + (units digit of 4) = ...”

“Let r=0, implying that no profit is made and that the oranges are sold at cost.
Let q=12, implying that the cost for 12 oranges is $12, with the result that the cost per orange = $1.
1.66 dozen = (5/3)(12) = 20 oranges.
Since the cost for 20 oranges = $20, p=20.
Thus:
5pq - 12r = (5*20*12) - ...”

“Here is an algebraic way to combine the two statements:
Let G = a game that results in a 2-point gain and L = a game that results in a 3-point loss.
Statement 1:
Since the played games yield a total of 4 points beyond the intital 100 points, we get:
2G - 3L = 4
2G = 4 + 3L
Note:
Since the ...”

“Goal:
To MAXIMIZE the number of nonfiction books.
Since the fraction of hardcover books that are nonfiction (2/3) is greater than the fraction of softcover books that are nonfiction (1/4), the number of nonfiction books will be maximized if we must MAXIMIZE THE NUMBER OF HARDCOVER BOOKS.
...”

“Case 1: One daughter in the front passenger seat:
Since one of the 2 parents must drive, number of choices for the driver''s seat = 2.
Since either of the 2 daughters can be in the front passenger seat, number of choices = 2.
Number of ways to arrange the 3 remaining people = 3! = 6.
To combine ...”

“Plug in for x a value that is easy to convert from meters to kilometers.
Let x = 1000 meters per second.
Since 1000 meters = 1 kilometer, this rate = 1 kilometer per second.
Since there are 3600 seconds in an hour, 1 kilometer per second = 3600 kilometers per hour.
Thus, y = 3600. This is ...”

“Sum of the 4 numbers = (quantity)(average) = 4*30 = 120.
Statement 1:
Case 1: The four numbers are 32, 31, 30, 27
In this case, two of the numbers are greater than 30.
Case 2: The four numbers are 33, 32, 31, 24
In this case, three of the numbers are greater than 30.
INSUFFICENT.
...”

“Statement 1:
Case 1: 1 sweater is sold for $270
Case 2: 3 sweaters are sold for $90 each
Since the number of sweaters sold can be different values, INSUFFICIENT.
Statement 2:
Since the $30 markup is 1/2 the cost of each sweater, the cost of each sweater = 60.
Thus, the selling price of ...”

“If x and y are equal, then their LCM = x = y.
Thus, x+y can be the LCM of x and y only if x and y are NOT equal.
If x+y is the LCM of x and y, then dividing x+y by x or y must yield an INTEGER.
If we divide x+y by x. we get:
(x+y)/x = x/x + y/x = 1 + y/x.
The expression in blue will be an ...”

“This problem is about TRAILING 0''s: the number of 0''s at the end of a large product.
Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of N will yield a 0 at the end of the integer representation of N..
N=5⁵ * 10¹⁰ * 15¹⁵ * 20²⁰ * 25²⁵ * 30³⁰ ...”

“x = 10% gravel
y = 2% gravel.
z = the MIXTURE of x and y = 5% gravel.
To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the ...”

“Statement 1:
Since ∠C=∠M=90 and ∠ABC=∠KLM, the remaining two angles are also equal:
∠BAC=∠LKM.
Triangles with the same combination of angles are SIMILAR.
In similar triangles, corresponding sides in the SAME RATIO.
Here, AB and KL are corresponding sides, since each is a ...”

“Statement 1:
Since ∠C=∠M=90 and ∠ABC=∠KLM, the remaining two angles are also equal:
∠BAC=∠LKM.
Triangles with the same combination of angles are SIMILAR.
In similar triangles, corresponding sides in the SAME RATIO.
Here, AB and KL are corresponding sides, since each is a ...”

“P(sibling pair) = (total number of sibling pairs)/(total number of possible pairs).
Total number of possible pairs:
There are 1000 juniors and 800 seniors.
Total number of ways to combine 1 junior with 1 senior = 1000*800 = 800,000.
Total number of sibling pairs = 60.
Thus:
...”

“Statement 1:
100z = 0.2, 1.2, 2.2...
Dividing every value by 100, we get the following options for z:
z = 0.002, 0.012, 0.022...
Since the hundredth digit of z can be different values, INSUFFICIENT.
Every value in the blue list above also satisfies Statement 2.
Thus -- even when the ...”

“Regular day:
Let r = the regular rate and t = the regular time, implying that the distance to the office = rt.
Last Wednesday:
Since Mr. David drives 25% faster -- 5/4 of his regular speed -- the rate = (5/4)r.
Since Mr. David leaves 30 minutes late -- reducing the time by 30 minutes -- the ...”

“To organize the data, use a DOUBLE-MATRIX.
10% of the people do not have a university diploma but have a job of their choice.
The following matrix is yielded:
https://s33.postimg.cc/ouzby26ln/matrix_diploma_job_1.png
40% people have a job of their choice.
The following matrix is yielded:
...”

“Since Deb drives for 3/4 of an hour at a rate of 40 mph, the driving distance to work = rt = (40)(3/4) = 30 miles.
Since the biking distance is 20% less than the driving distance, the biking distance = 30 - (1/5)(30) = 24 miles.
To guarantee an on-time arrival at even the least possible biking ...”

“Statement 1:
Here, Steven''s time can be any nonnegative value.
INSUFFICIENT.
Statement 2:
Rate and time have a RECIPROCAL RELATIONSHIP.
Since George''s speed in 2/3 Steven''s speed, George''s time is 3/2 Steven''s time.
Since George''s time is 3.5 hours, we get:
3.5 = (3/2)t
7 = 3t
7/3 = ...”

“(-1)^odd = -1.
(-1)^even = 1.
The exponents for the expression in blue are 4 consecutive integers -- n, n+1, n+2, n+3 -- implying that two of the exponents will be ODD, while the other two will be EVEN.
Thus, two of the terms in the blue expression must be equal to -1, while the other two must be ...”

“A box of balls originally contained 2 blue balls for every red ball.
Let the number of red balls = x and the number blue balls = 2x, implying that the total number of balls = x+2x = 3x.
After 12 red balls were added to the box, the ratio of red balls to blue balls became 5 to 2.
Since 12 red ...”

“P(at least one of the 2 selected roads is at least 5 miles long) = 1 - P(neither of the 2 selected roads is at least 5 miles long)
From A to B:
Since 2/3 of the roads are at least 5 miles long, 1/3 are not.
Thus, the probability of selecting a road that is not at least 5 miles long = 1/3.
...”

“To calculate the sum of an integer''s positive factors:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. Sum of the factors = (1+a¹+ a²+a³+...+a^p)(1+b¹+ b²+b³+...+b^q)(1+c¹+ c²+c³+...+c^r)...
What is the sum of the positive factors of ...”

“The statement in red does not accurately reflect the information in Statement 2.
Statement 2: People under the age of 20 spent $2.2 billion MORE on movie tickets than did people over the age of 50.
Here, the total amount spent by people under the age of 20 ≠ $2.2 billion.
The usage of MORE ...”

“This problem is invalid.
Since the only conditions are that six terms must be positive and odd and have a total of 13 digits, an infinite number of cases are possible.
Here are two options:
11, 13, 15, 17, 19, 101
13, 11, 15, 17, 19, 101
Since the sequence does not have to be ascending, any of ...”

“Average of the 3 consecutive integers = sum/quantity = 54/3 = 18.
For any set of consecutive integers, average = median.
Thus, the median of the 3 integers = 18, implying that the 3 integers are 17, 18, and 19.
Product of the smallest and largest = 17*19 = integer with a units digit of 3.
The ...”

“Time and rate are RECIPROCALS.
x = the REGULAR speed.
1.25x = the FASTER speed.
1.25x = (125/100)x = (5/4)x.
5/4 the rate implies 4/5 the time.
Thus:
The time needed at the FASTER speed is equal to 4/5 the time needed at the REGULAR speed.
The question stems asks for the following ratio:
...”

“For only 2 colors to remain after 4 marbles have been removed, the 4 selected marbles must be of the same color.
The first selected marble can be of ANY COLOR.
A good outcome will be yielded if the second, third and fourth marbles are of the SAME COLOR as the first.
P(2nd marble is of the same ...”

“For the solid to have four faces with the same dimensions, two opposing faces must be SQUARES, as in the following figure:https://preview.ibb.co/koZpb8/rectangular_solid_with_square_base.png
In the figure above:
The area of the square base and the area of the square top = L*L.
The areas of the ...”

“When an integer is divided by 100, the remainder will have the same units digit as the integer.
Thus, to determine which answer choice represents the remainder when 7⁸ is divided by 100, we need to know the units digit of 7⁸.
When an integer is raised to consecutive powers, the resulting units ...”

“We can PLUG IN THE ANSWERS, which represent the amount of profit.
Since Ed earns a flat salary of $1000 if the amount of profit does not exceed $8000 -- and all of the answer choices are less than 8000 -- Ed''s earnings = $1000.
Since John and Ed must earn the same amount, John must also earn ...”

“We can apply the SEPARATOR METHOD, which I describe here:
https://www.beatthegmat.com/combinations-t120668.html
To solve the problem above, we need 6 identical chocolates and 2 identical separators, as follows:
OO|OO|OO.
The number of ways to arrange 8 elements composed of 6 identical ...”

“This line of reasoning applies to a VERBing modifier preceded by CLAUSE + COMMA.
In C, making is preceded not by CLAUSE + COMMA but by a NOUN PHRASE (a part of a deal).
The referent for this noun phrase is unclear, as discussed in my earlier post.
As a result, a reader cannot be sure whether ...”

“The construction in red is acceptable when it serves to express how a subject CHANGES.
An OA in the OG for Verbal:
Its numbers are now five times greater than when the use of DDT was sharply restricted in the early 1970.
Here, the portion in blue serves to express how ITS NUMBERS have changed ...”

“To count the factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form Statement 1:
Test one case that also satisfies Statement 2.
Case 1: p=5, with the result that (3^n)(p^2) = 3⁴5²
Adding 1 to each exponent and multiplying, we get:
Number ...”

“Since the time difference yielded by the two speeds is an INTEGER -- 1 hour less -- the actual speed and hypothetical greater speed must both divide evenly into the 450-mile distance.
We can PLUG IN THE ANSWERS, which represent the actual speed.
Since A, B and E do not evenly into 450, eliminate ...”

“Statement 1:
Average for 4 of the 6 days = 100 per day.
Least possible average for the other 2 days = 80 per day.
Since there are MORE DAYS with an average of 100 per day than with an average of at least 80 per day, the average for all 6 days must be CLOSER TO 100 THAN TO 80.
Thus, the average ...”

“One way to evaluate Statement 1 is to test whether the value given in Statement 2 -- $5000 in sales -- is the ONLY value that will also satisfy Statement 1.
Statement 1: The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
Case 1: Let ...”

“Statement 1: X produced 30 bottles per minute.
Thus, the work produced by X in 240 minutes = r*t = 30*240.
No information about how much work was produced by Y.
INSUFFICIENT.
Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
Thus, for ...”

“Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? Yes.
If y= -1 and x = 1, is 1*(-1) > 0? No.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.
Statement 2: x < 2y-6
If y=1 and x = -10, is 1*(-10) > 0? No.
If y = 10 and x = 1, is 1*10 > ...”

“To count the factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)..
2700 = 2²3³5²
Adding 1 to each exponent and multiplying, we get:
Total number of factors = ...”

“Since $75 is 50% more than $50, the first 5 contributions were worth an average of $50.
Thus, the sum of the first 5 contributions = 5*50 = 250.
Since the average of all 6 contributions = $75, the sum of all 6 contributions = 6*75 = 450.
Thus, John''s contribution = (sum of all 6 contributions) - ...”

“Statement 1:
Make a list of options for m+1:
m+1 = 12, 15, 18, 21, 24, 27...
To get a list option for m, subtract 1 from every value in the list above:
m = 11, 14, 17, 20, 23, 26...
When any value in the resulting list is divided by 3, the remainder in every case is 2.
SUFFICIENT.
Statement ...”

“(1.5% of 5000) + (2.5% of 5000) = 75 + 125 = 200.
We can PLUG IN THE ANSWERS, which represent the total annual charge.
When the correct answer is plugged in, the cash back will be 2.6% of the total annual charge.
D: 26,000
Since 3% is earned on the amount over $10,000 -- in other words, since ...”

“Given ratio = S:C = 2:7.
The difference between the parts of the ratio = 7-2 = 5.
Since the actual difference between the number of cats and the number of spinsters is five times as great -- 25 -- each part of the ratio must be multiplied by a FACTOR OF 5:
S:C = (2*5) : (7*5) = 10:35, with the ...”

“Since the resulting ratio = A:B = 3:10, and all of the values in the problem are integers, the correct answer must yield a multiple of 10 when added to the 2 original liters in B.
Only D is viable:
48+2 = 50 liters.
The correct answer is D.”

“Statements combined:
https://preview.ibb.co/i0YOtd/plane.png
The dotted green line indicates the plane''s position at 12pm.
The blue right triangle indicates the plane''s position at 3pm.
The two dotted red lines show positions for the island that are 450 miles from the plane''s position at ...”

“If the average age of the students is exactly 30, then the sum of the 60 ages = 60*30 = 1800.
Implication:
For the average age to be GREATER THAN 30, the SUM of the 60 ages must be GREATER THAN 1800.
Question stem, rephrased:
Is the sum of the 60 ages greater than 1800?
Statement 1:
Since ...”

“Normal day:
4pm --> The wife leaves home and drives to the station.
5pm --> The husband''s train and the wife both arrive at the station.
6pm --> The husband and wife arrive home.
Implication:
The normal driving time in each direction = 60 minutes.
Today:
Since the wife and the ...”

“Since there are 12 people, the first person selected can be paired with any of the 11 other people, yielding 11 POSSIBLE PAIRS.
Since 2 of the 12 people have been selected thus far, the number of people remaining = 12-2 = 10.
Since 10 people remain, the next person selected can be paired with ...”

“Since 4080 is between 5% and 10% of 60,000, it is likely that x and y are between 5 and 10.
Statement 1: x = (3/4)y
It''s possible that x=6 and y=8 or that x=6.6 and that y=8.8.
To accommodate the desired combination of percentages, we could simply adjust the amount invested at each percentage ...”

“Let A = A''s rate and B = Brian''s rate.
Ashok has to CATCH-UP by 30 miles.
The CATCH-UP rate is equal to the DIFFERENCE between the two rates.
If A = 3mph, while B = 2mph, then every hour A walks 1 more mile than B, with the result that every hour A catches up by 1 mile -- the DIFFERENCE ...”

“When the two statements are combined, the 2 additional items produced this week result in an earnings increase of $30 (from $480 to $510).
Thus, the amount earned by each of the 2 additional items produced this week = 30/2 = 15.
It is possible that these 2 additional items were paid at the ...”